arXiv subjects

Vitaly Aksenov

Publications and source records attributed to Vitaly Aksenov.

At least 19 recordsLinked to original sources

arXiv2026

Semantic Lock: Synchronization Based on the Analysis of the Operation Conflict Graph

This paper presents a new lock, SemanticLock, based on the conflict graph between operations. We can consider it a generalization of a read-write lock where conflicts exist between write operations and all other operations. We demonstrate the effectiveness of our lock in two applications. In the first, we design a toy data structure: an array supporting point queries and different range queries. In the second, potentially of greater interest, we augment an existing concurrent data structure, ConcurrentHashMap, with additional long-running operations.

cs.DC↗

arXiv2026

Concurrent Splay-Based Tree

Most work on efficient concurrent ordered indices, such as concurrent binary search trees, B-trees, skip lists, etc., has focused on data structures that provide good \emph{worst-case} guarantees. In real workloads, objects are often accessed at different rates, since access distributions may be non-uniform. Many efficient distribution-adaptive data structures exist in the sequential case; however, they are often complicated to make efficient in the concurrent case. The most prominent distribution-adaptive data structure is Splay Tree. Its most important advantage is that it does not store any balancing information and provides a reasonable performance improvement on extremely skewed workloads, such as Zipfian workloads. This paper proposes a splay-like rotation design for concurrent binary search trees. Instead of moving an accessed node to the root, rotations use two depth thresholds that are based on the static-optimality complexity computed from the number of accesses to the node: a node is rotated only when it is substantially deeper than the upper threshold, and rotations of the node stop before reaching the lower threshold. This design aims to preserve the main practical benefit of splaying on skewed workloads while reducing contention near the root. We present two variants of the rotation design: one using an exact 64-bit access counter per node and one using a 6-bit approximate counter. We prove static optimality for the corresponding sequential read-only tree and evaluate both rotation designs by implementing them on top of the concurrent AVL tree of Bronson et al. Our experiments show that the approach can improve throughput on several skewed workloads.

cs.DC↗

arXiv2026

Compression is all you need: Modeling Mathematics

Human mathematics (HM), the mathematics humans discover and value, is a vanishingly small subset of formal mathematics (FM), the totality of all valid deductions. We argue that HM is distinguished by its compressibility through hierarchically nested definitions, lemmas, and theorems. We model this with monoids. A mathematical deduction is a string of primitive symbols; a definition or theorem is a named substring or macro whose use compresses the string. In the free abelian monoid $A_n$, a logarithmically sparse macro set achieves exponential expansion of expressivity. In the free non-abelian monoid $F_n$, even a polynomially-dense macro set only yields linear expansion; superlinear expansion requires near-maximal density. We test these models against MathLib, a large Lean~4 library of mathematics that we take as a proxy for HM. Each element has a depth (layers of definitional nesting), a wrapped length (tokens in its definition), and an unwrapped length (primitive symbols after fully expanding all references). We find unwrapped length grows exponentially with both depth and wrapped length; wrapped length is approximately constant across all depths. These results are consistent with $A_n$ and inconsistent with $F_n$, supporting the thesis that HM occupies a polynomially-growing subset of the exponentially growing space FM. We discuss how compression, measured on the MathLib dependency graph, and a PageRank-style analysis of that graph can quantify mathematical interest and help direct automated reasoning toward the compressible regions where human mathematics lives.

cs.AI↗

arXiv2026

Semantic Conflict Model for Collaborative Data Structures

Digital collaboration systems support asynchronous work over replicated data, where conflicts arise when concurrent operations cannot be unambiguously integrated into a shared history. While Conflict-Free Replicated Data Types (CRDTs) ensure convergence through built-in conflict resolution, this resolution is typically implicit and opaque to users, whereas existing reconciliation techniques often rely on centralized coordination. This paper introduces a conflict model for collaborative data structures that enables explicit, local-first conflict resolution without central coordination. The model identifies conflicts using semantic dependencies between operations and resolves them by rebasing conflicting operations onto a reconciling operation via a three-way merge over a replicated journal. We demonstrate our approach on collaborative registers, including an explicit formulation of the Last-Writer-Wins Register and a multi-register entity supporting semi-automatic reconciliation.

cs.DC↗

arXiv2025

Basic Lock Algorithms in Lightweight Thread Environments

Traditionally, multithreaded data structures have been designed for access by the threads of Operating Systems (OS). However, implementations for access by programmable alternatives known as lightweight threads (also referred to as asynchronous calls or coroutines) have not been thoroughly studied. The main advantage of lightweight threads is their significantly lower overhead during launch and context switching. However, this comes at a cost: to achieve proper parallelism, context switches must be manually invoked in the code; without these switches, new lightweight threads will never be executed. In this paper, we focus on the simplest multithreaded data structure: a mutex (also known as a lock). We demonstrate that original implementations for OS threads cannot be used effectively in this new context due to the potential for deadlocks. Furthermore, correctness is not the only concern. In certain languages, such as C++, there are various lightweight thread libraries, each with different implementations and interfaces, which necessitate distinct lock implementations. In this work, we present a modification of TTAS and MCS locks for the use from lightweight threads and demonstrate that the two context switch mechanisms of lightweight threads, yielding and sleeping, are crucial. However, the performance of TTAS and MCS may differ significantly depending on the settings. If one wants to have a lock that works well for any library, we suggest using the cohort lock, which strikes a balance between MCS and TTAS by utilizing several MCS queues with a common TTAS.

cs.DC↗

arXiv2025

Model-based Testing of Practical Distributed Systems in Actor Model

Designing and implementing distributed systems correctly can be quite challenging. Although these systems are often accompanied by formal specifications that are verified using model-checking techniques, a gap still exists between the implementation and its formal specification: there is no guarantee that the implementation is free of bugs. To bridge this gap, we can use model-based testing. Specifically, if the model of the system can be interpreted as a finite-state automaton, we can generate an exhaustive test suite for the implementation that covers all possible states and transitions. In this paper, we discuss how to efficiently generate such a test suite for distributed systems written in the actor model. Importantly, our approach does not require any modifications to the code or interfering with the distributed system execution environment. As an example, we verified an implementation of a replication algorithm based on Viewstamped Replication, which is used in a real-world system.

cs.DC↗

arXiv2024

Skip Hash: A Fast Ordered Map Via Software Transactional Memory

Scalable ordered maps must ensure that range queries, which operate over many consecutive keys, provide intuitive semantics (e.g., linearizability) without degrading the performance of concurrent insertions and removals. These goals are difficult to achieve simultaneously when concurrent data structures are built using only locks and compare-and-swap objects. However, recent innovations in software transactional memory (STM) allow programmers to assume that multi-word atomic operations can be fast and simple. This paper introduces the skip hash, a new ordered map designed around that assumption. It combines a skip list and a hash map behind a single abstraction, resulting in $O(1)$ overheads for most operations. The skip hash makes use of a novel range query manager -- again leveraging STM -- to achieve fast, linearizable range queries that do not inhibit scalability. In performance evaluation, we show that the skip hash outperforms the state of the art in almost all cases. This places the skip hash in the uncommon position of being both exceedingly fast and exceedingly simple.

cs.DC↗

arXiv2024

Toward Self-Adjusting k-ary Search Tree Networks

Datacenter networks are becoming increasingly flexible with the incorporation of new networking technologies, such as optical circuit switches. These technologies allow for programmable network topologies that can be reconfigured to better serve network traffic, thus enabling a trade-off between the benefits (i.e., shorter routes) and costs of reconfigurations (i.e., overhead). Self-Adjusting Networks (SANs) aim at addressing this trade-off by exploiting patterns in network traffic, both when it is revealed piecewise (online dynamic topologies) or known in advance (offline static topologies). In this paper, we take the first steps toward Self-Adjusting k-ary tree networks. These are more powerful generalizations of existing binary search tree networks (like SplayNets), which have been at the core of SAN designs. k-ary search tree networks are a natural generalization offering nodes of higher degrees, reduced route lengths for a fixed number of nodes, and local routing in spite of reconfigurations. We first compute an offline (optimal) static network for arbitrary traffic patterns in $O(n^3 \cdot k)$ time via dynamic programming, and also improve the bound to $O(n^2 \cdot k)$ for the special case of uniformly distributed traffic. Then, we present a centroid-based topology of the network that can be used both in the offline static and the online setting. In the offline uniform-workload case, we construct this quasi-optimal network in linear time $O(n)$ and, finally, we present online self-adjusting k-ary search tree versions of SplayNet. We evaluate experimentally our new structure for $k=2$ (allowing for a comparison with existing SplayNets) on real and synthetic network traces. Our results show that this approach works better than SplayNet in most of the real network traces and in average to low locality synthetic traces, and is only little inferior to SplayNet in all remaining traces.

cs.NI↗

arXiv2024

Derivative-based regularization for regression

In this work, we introduce a novel approach to regularization in multivariable regression problems. Our regularizer, called DLoss, penalises differences between the model's derivatives and derivatives of the data generating function as estimated from the training data. We call these estimated derivatives data derivatives. The goal of our method is to align the model to the data, not only in terms of target values but also in terms of the derivatives involved. To estimate data derivatives, we select (from the training data) 2-tuples of input-value pairs, using either nearest neighbour or random, selection. On synthetic and real datasets, we evaluate the effectiveness of adding DLoss, with different weights, to the standard mean squared error loss. The experimental results show that with DLoss (using nearest neighbour selection) we obtain, on average, the best rank with respect to MSE on validation data sets, compared to no regularization, L2 regularization, and Dropout.

cs.LG↗

arXiv2024

In the Search of Optimal Tree Networks: Hardness and Heuristics

Demand-aware communication networks are networks whose topology is optimized toward the traffic they need to serve. These networks have recently been enabled by novel optical communication technologies and are investigated intensively in the context of datacenters. In this work, we consider networks with one of the most common topologies~ -- a binary tree. We show that finding an optimal demand-aware binary tree network is NP-hard. Then, we propose optimization algorithms that generate efficient binary tree networks on real-life and synthetic workloads.

cs.NI↗

arXiv2024

Trigram-Based Persistent IDE Indices with Quick Startup

One common way to speed up the find operation within a set of text files involves a trigram index. This structure is merely a map from a trigram (sequence consisting of three characters) to a set of files which contain it. When searching for a pattern, potential file locations are identified by intersecting the sets related to the trigrams in the pattern. Then, the search proceeds only in these files. However, in a code repository, the trigram index evolves across different versions. Upon checking out a new version, this index is typically built from scratch, which is a time-consuming task, while we want our index to have almost zero-time startup. Thus, we explore the persistent version of a trigram index for full-text and key word patterns search. Our approach just uses the current version of the trigram index and applies only the changes between versions during checkout, significantly enhancing performance. Furthermore, we extend our data structure to accommodate CamelHump search for class and function names.

cs.SE↗

arXiv2024

Memory Bounds for Concurrent Bounded Queues

Concurrent data structures often require additional memory for handling synchronization issues in addition to memory for storing elements. Depending on the amount of this additional memory, implementations can be more or less memory-friendly. A memory-optimal implementation enjoys the minimal possible memory overhead, which, in practice, reduces cache misses and unnecessary memory reclamation. In this paper, we discuss the memory-optimality of non-blocking bounded queues. Essentially, we investigate the possibility of constructing an implementation that utilizes a pre-allocated array to store elements and constant memory overhead, e.g., two positioning counters for enqueue(..) and dequeue() operations. Such an implementation can be readily constructed when the ABA problem is precluded, e.g., assuming that the hardware supports LL/SC instructions or all inserted elements are distinct. However, in the general case, we show that a memory-optimal non-blocking bounded queue incurs linear overhead in the number of concurrent processes. These results not only provide helpful intuition for concurrent algorithm developers but also open a new research avenue on the memory-optimality phenomenon in concurrent data structures.

cs.DC↗

arXiv2023

On the Complexity of the Virtual Network Embedding in Specific Tree Topologies

Virtual networks are an innovative abstraction that extends cloud computing concepts to the network: by supporting bandwidth reservations between compute nodes (e.g., virtual machines), virtual networks can provide a predictable performance to distributed and communication-intensive cloud applications. However, in order to make the most efficient use of the shared resources, the Virtual Network Embedding (VNE) problem has to be solved: a virtual network should be mapped onto the given physical network so that resource reservations are minimized. The problem has been studied intensively already and is known to be NP-hard in general. In this paper, we revisit this problem and consider it on specific topologies, as they often arise in practice. To be more precise, we study the weighted version of the VNE problem: we consider a virtual weighted network of a specific topology which we want to embed onto a weighted network with capacities and specific topology. As for topologies, we consider most fundamental and commonly used ones: line, star, $2$-tiered star, oversubscribed $2$-tiered star, and tree, in addition to also considering arbitrary topologies. We show that typically the VNE problem is NP-hard even in more specialized cases, however, sometimes there exists a polynomial algorithm: for example, an embedding of the oversubscribed $2$-tiered star onto the tree is polynomial while an embedding of an arbitrary $2$-tiered star is not.

cs.CC↗

arXiv2023

Wait-free Trees with Asymptotically-Efficient Range Queries

Tree data structures, such as red-black trees, quad trees, treaps, or tries, are fundamental tools in computer science. A classical problem in concurrency is to obtain expressive, efficient, and scalable versions of practical tree data structures. We are interested in concurrent trees supporting range queries, i.e., queries that involve multiple consecutive data items. Existing implementations with this capability can list keys in a specific range, but do not support aggregate range queries: for instance, if we want to calculate the number of keys in a range, the only choice is to retrieve a whole list and return its size. This is suboptimal: in the sequential setting, one can augment a balanced search tree with counters and, consequently, perform these aggregate requests in logarithmic rather than linear time. In this paper, we propose a generic approach to implement a broad class of range queries on concurrent trees in a way that is wait-free, asymptotically efficient, and practically scalable. The key idea is a new mechanism for maintaining metadata concurrently at tree nodes, which can be seen as a wait-free variant of hand-over-hand locking (which we call hand-over-hand helping). We implement, test, and benchmark a balanced binary search tree with wait-free insert, delete, contains, and count operations, returning the number of keys in a given range which validates the expected speedups because of our method in practice.

cs.DB↗

arXiv2023

Efficient Self-Adjusting Search Trees via Lazy Updates

Self-adjusting data structures are a classic approach to adapting the complexity of operations to the data access distribution. While several self-adjusting variants are known for both binary search trees and B-Trees, existing constructions come with limitations. For instance, existing works on self-adjusting B-Trees do not provide static-optimality and tend to be complex and inefficient to implement in practice. In this paper, we provide a new approach to build efficient self-adjusting search trees based on state-of-the-art non-adaptive structures. We illustrate our approach to obtain a new efficient self-adjusting Interpolation Search Tree (IST) and B-Tree, as well as a new self-adjusting tree called the Log Tree. Of note, our self-adjusting IST has expected complexity in $O(\log \frac{\log m}{\log ac(x)})$, where $m$ is the total number of requests and $ac(x)$ is the number of requests to key $x$. Our technique leads to simple constructions with a reduced number of pointer manipulations: this improves cache efficiency and even allows an efficient concurrent implementation.

cs.DS↗

arXiv2023

Parallel-batched Interpolation Search Tree

A sorted set (or map) is one of the most used data types in computer science. In addition to standard set operations, like Insert, Remove, and Contains, it can provide set-set operations such as Union,Intersection, and Difference. Each of these set-set operations is equivalent to some batched operation: the data structure should be able to execute Insert, Remove, and Contains on a batch of keys. It is obvious that we want these "large" operations to be parallelized. These sets are usually implemented with the trees of logarithmic height, such as 2-3 trees, treaps, AVL trees, red-black trees, etc. Until now, little attention was devoted to data structures that work asymptotically better under several restrictions on the stored data. In this work, we parallelize Interpolation Search Tree which is expected to serve requests from a smooth distribution in doubly-logarithmic time. Our data structure of size n performs a batch of m operations in O(m log log n) work and poly-log span.

cs.DC↗

arXiv2023

Benchmark Framework with Skewed Workloads

In this work, we present a new benchmarking suite with new real-life inspired skewed workloads to test the performance of concurrent index data structures. We started this project to prepare workloads specifically for self-adjusting data structures, i.e., they handle more frequent requests faster, and, thus, should perform better than their standard counterparts. We looked over the commonly used suites to test performance of concurrent indices trying to find an inspiration: Synchrobench, Setbench, YCSB, and TPC - and we found several issues with them. The major problem is that they are not flexible: it is difficult to introduce new workloads, it is difficult to set the duration of the experiments, and it is difficult to change the parameters. We decided to solve this issue by presenting a new suite based on Synchrobench. Finally, we highlight the problem of measuring performance of data structures. We show that the relative performance of data structures highly depends on the workload: it is not clear which data structure is best. For that, we take three state-of-the-art concurrent binary search trees and run them on the workloads from our benchmarking suite. As a result, we get six experiments with all possible relative performance of the chosen data structures.

cs.DC↗

arXiv2023

Self-Adjusting Linear Networks with Ladder Demand Graph

Self-adjusting networks (SANs) have the ability to adapt to communication demand by dynamically adjusting the workload (or demand) embedding, i.e., the mapping of communication requests into the network topology. SANs can thus reduce routing costs for frequently communicating node pairs by paying a cost for adjusting the embedding. This is particularly beneficial when the demand has structure, which the network can adapt to. Demand can be represented in the form of a demand graph, which is defined by the set of network nodes (vertices) and the set of pairwise communication requests (edges). Thus, adapting to the demand can be interpreted by embedding the demand graph to the network topology. This can be challenging both when the demand graph is known in advance (offline) and when it revealed edge-by-edge (online). The difficulty also depends on whether we aim at constructing a static topology or a dynamic (self-adjusting) one that improves the embedding as more parts of the demand graph are revealed. Yet very little is known about these self-adjusting embeddings. In this paper, the network topology is restricted to a line and the demand graph to a ladder graph, i.e., a $2^n$ grid, including all possible subgraphs of the ladder. We present an online self-adjusting network that matches the known lower bound asymptotically and is $12$-competitive in terms of request cost. As a warm up result, we present an asymptotically optimal algorithm for the cycle demand graph. We also present an oracle-based algorithm for an arbitrary demand graph that has a constant overhead.

cs.NI↗